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The intention of this paper is to examine the principles and methods that have been proposed for solving the problem of which it treats, with the view of obviating what is obscure and exceptionable in the investigation usually given of it. The principle first advanced by Huyghens is clearly demonstrate, and is attended with no difficulty. This principle requires that the resultant of the forces in action at the surface of a fluid in equilibrium and at liberty, shall be perpendicular to that surface: and it is grounded on this, that the forces must have no tendency to move a particle in any direction upon the surface, that is, in a plane touching the surface.

On the conditions of equilibrium of an incompressible fluid, the particles of which are acted upon by accelerating forces